An investigation involves the explanation, analysis and generalization
of a mathematical problem.
example, a student investigated the problem:
How many squares are there on a chessboard ?
First the student realized it could be interpreted to obtain
an answer other than 64. She then simplified the problem by
starting with small chessboards (1 by1, 2 by 2 etc.). From
these special cases a pattern emerged and a conjecture was
made. She then went on to prove the conjecture and was able
to generalise it to obtain a formula for the number of squares
on an n by n board. Other problems then suggested themselves,
How many rectangles are there on a chessboard
Can the problem be extended to three dimension ?